Question : If 6A = 4B = 9C; what is A : B : C?

Option 1: $6:4:9$

Option 2: $9:4:6$

Option 3: $4:9:6$

Option 4: $6:9:4$

Question : If A : B = 2 : 3 and B : C = 3 : 7, then (A + B) : (B + C) : (C + A) is:

Option 1: 4 : 8 : 9

Option 2: 5 : 8 : 9

Option 3: 5 : 10 : 9

Option 4: 4 : 10 : 9

Question : If $a+b+c=7$ and $a^3+b^3+c^3-3abc=175$, then what is the value of $(a b+b c+c a)$?

Option 1: 8

Option 2: 9

Option 3: 7

Option 4: 6

Question : If $a: b: c=\frac{1}{4}: \frac{1}{3}: \frac{1}{2}$, then $\frac{a}{b}: \frac{b}{c}: \frac{c}{a}=$?

Option 1: 12 : 9 : 8

Option 2: 9 : 8 : 24

Option 3: 8 : 9 : 24

Option 4: 9 : 12 : 8

Question : If $a+b+c=6$ and $a^2+b^2+c^2=14$, then what is the value of $(a-b)^2+(b-c)^2+(c-$ a) ${ }^2$?

Option 1: –8

Option 2: 8

Option 3: 10

Option 4: 6